Throughout his life, Hegel showed great interest in physics and mathematics. His most sustained, surviving treatment of Euclidean geometry is his early work ‘Geometrische Studien’, which he completed while he was a private tutor [Hoffmeister] in Frankfurt, shortly before leaving for Jena to join Schelling. GS is not easy reading, but despite that, it seems to me that Hegel presents in it a remarkably erudite as well as interesting and insightful critique of geometry. He investigates some of the themes from the foundations of geometry, in particular from the first book of the Elements of Euclid. Like the mathematical philosophies of Kant and Frege, Hegel's understanding of geometry is conceptually based, but unlike them, it is also grounded in the classical Greek philosophy of mathematics, which achieved its definitive expression in Proclus's great commentary on Euclid 1. Much of this classical philosophy of geometry is forgotten nowadays, under the influence of the great modern mathematical philosophers (in particular, Cantor, Frege and Gödel). In my view, it well deserves reconsideration, especially since, as illustrated by Gödel's incompleteness theorems, modern mathematical philosophy has failed in its attempt to ground mathematics within the framework of formal systems.
Much of GS has not survived, and what remains is condensed and fragmentary. It seems that originally, Hegel covered all of the propositions of Euclid 1 rather than just the 14 propositions (1-12, 26, 29) that are covered in what remains of the original GS. I have given detailed treatment of GS together with related material in Hegel's Jena dissertation elsewhere (Paterson 2004/2005). The objective of the present paper is to introduce the translation of GS.